9 PDF - Pavel K. Smrz, Illusion of space-time and quantum mechanics

Illusion of space-time and quantum mechanics

1School of Mathematical and Physical Sciences, The University of Newcastle, Newcastle, New South Wales 2308, Australia

This article amalgamates some results published previously by the author with their natural extension. The discussion is also more detailed than in the preceding papers and the mathematical introduction more accessible to a wider readership. The basic idea concerns a construction of the classical space-time from a de Sitter linear connection on a five-dimensional manifold when the transformations of the reference cross section in its bundle of linear frames are restricted to the Lorentz subgroup. The restriction is related to the classical space-time measurements. When the absence of measurements allows the restriction to be lifted, the dimension of the constructed space can be reduced to time only. Since the five-dimensional geometry contains a fundamental unit of length, assumed to be the Planck length, a link with quantum theory can be established. The nonlocal behavior of particles is thus associated with a radically changed geometry within unobserved regions of space-time. The quantum mechanical phase plane has a geometrical meaning within the five-dimensional geometry. The requirement that the geometry allows the space-time to be constructed puts conditions on the linear connection of the five-dimensional manifold as well as on the resulting geometry of the constructed space-time. The simplest and at the same time most restrictive way to satisfy the conditions assumes that all connection components in the direction of ∂/∂x5 are zero and leads to the equation Rαβ=(1/l2)gαβ on the five-dimensional manifold and Einstein’s vacuum equations on the constructed space-time. When the Lorentz components of the connection A5ji in the direction of ∂/∂x5 are not zero, there exists a set of equations that reduce to the Einstein–Maxwell equations on the space-time with A5ji playing the role of the electromagnetic field tensor.